Why are tree-based models more widely used in Medical Diagnosis?
One possible reason may have something to do with the scrutability of models, as described in the first few paragraphs of this article.  It presents a case study of a hospital whose policy was to send asthma sufferers to an intensive care unit; the intensive care meant they were less likely to develop pneumonia and therefore the data showed that people with asthma were less likely to have pneumonia.

Essentially, since machine learning models learn false relationships if the data are in any way flawed, it is beneficial to be able to "debug" them.  The processes by which decision trees make their decisions, and the reasons for making them, are more readily visible than in other models - particularly neural networks - which makes errors such as the example given in the article more likely to be picked up and corrected.